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Simplifying 94 + -88x + 13x2 = 0 Solving 94 + -88x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 7.230769231 + -6.769230769x + x2 = 0 Move the constant term to the right: Add '-7.230769231' to each side of the equation. 7.230769231 + -6.769230769x + -7.230769231 + x2 = 0 + -7.230769231 Reorder the terms: 7.230769231 + -7.230769231 + -6.769230769x + x2 = 0 + -7.230769231 Combine like terms: 7.230769231 + -7.230769231 = 0.000000000 0.000000000 + -6.769230769x + x2 = 0 + -7.230769231 -6.769230769x + x2 = 0 + -7.230769231 Combine like terms: 0 + -7.230769231 = -7.230769231 -6.769230769x + x2 = -7.230769231 The x term is -6.769230769x. Take half its coefficient (-3.384615385). Square it (11.45562130) and add it to both sides. Add '11.45562130' to each side of the equation. -6.769230769x + 11.45562130 + x2 = -7.230769231 + 11.45562130 Reorder the terms: 11.45562130 + -6.769230769x + x2 = -7.230769231 + 11.45562130 Combine like terms: -7.230769231 + 11.45562130 = 4.224852069 11.45562130 + -6.769230769x + x2 = 4.224852069 Factor a perfect square on the left side: (x + -3.384615385)(x + -3.384615385) = 4.224852069 Calculate the square root of the right side: 2.055444494 Break this problem into two subproblems by setting (x + -3.384615385) equal to 2.055444494 and -2.055444494.Subproblem 1
x + -3.384615385 = 2.055444494 Simplifying x + -3.384615385 = 2.055444494 Reorder the terms: -3.384615385 + x = 2.055444494 Solving -3.384615385 + x = 2.055444494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.384615385' to each side of the equation. -3.384615385 + 3.384615385 + x = 2.055444494 + 3.384615385 Combine like terms: -3.384615385 + 3.384615385 = 0.000000000 0.000000000 + x = 2.055444494 + 3.384615385 x = 2.055444494 + 3.384615385 Combine like terms: 2.055444494 + 3.384615385 = 5.440059879 x = 5.440059879 Simplifying x = 5.440059879Subproblem 2
x + -3.384615385 = -2.055444494 Simplifying x + -3.384615385 = -2.055444494 Reorder the terms: -3.384615385 + x = -2.055444494 Solving -3.384615385 + x = -2.055444494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.384615385' to each side of the equation. -3.384615385 + 3.384615385 + x = -2.055444494 + 3.384615385 Combine like terms: -3.384615385 + 3.384615385 = 0.000000000 0.000000000 + x = -2.055444494 + 3.384615385 x = -2.055444494 + 3.384615385 Combine like terms: -2.055444494 + 3.384615385 = 1.329170891 x = 1.329170891 Simplifying x = 1.329170891Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.440059879, 1.329170891}
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